Review of rock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjørndalen (Svalbard)

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David Viejo MariñoRock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjorndalen (Svalbard) NTNU Norwegian University of Science and Technology Faculty of Engineering Department of Civil and Environmental Engineering

Master ’s thesis

David Viejo Mariño

Review of rock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjorndalen

(Svalbard)

Master’s thesis in Cold Climate Engineering

Supervisor: Arne Aalberg (UNIS), Knut Vilhelm Hoyland (NTNU) & Ida Lykke Fabricius (DTU)

September 2020

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David Viejo Mariño

Review of rock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjorndalen

(Svalbard)

Master’s thesis in Cold Climate Engineering

Supervisor: Arne Aalberg (UNIS), Knut Vilhelm Hoyland (NTNU) & Ida Lykke Fabricius (DTU)

September 2020

Norwegian University of Science and Technology Faculty of Engineering

Department of Civil and Environmental Engineering

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Acknowledgments

I want to thank all my supervisors and reviewers for their feedback which helped into making this thesis better.

Arne Aalberg my main supervisor for all the help, the projects and trips we did together my stay in Svalbard and my thesis would not have been the same.

Nataly Marchenko for her time and help to obtain the most important digital terrain model and 3D shapes of the rocks, could not have done it without you.

Amir M Kaynia and Steve Gibbons from NGI for their help with seismic data

Jean-Dominique from RocPro 3D and the RAMMS team for providing me with licenses for their software

Last but not least all the friends I did up here and moments spent together being them in the wild, at Nybyen or Sjøskrenten. Because sleeping outside at 21º in the arctic is uncommon, a mirror will never be just a mirror and well… just SEND IT.

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Abstract

Geotechnical hazards represent a threat to communities around the world. The area between Vestpynten and Bjørndalen in the artic archipelago of Svalbard presents several geotechnical hazards that had produced recent incidents related with avalanches, debris flow and rockfalls. This area is used by the local population with leisure purposes. Due to that and the risk associated, a risk assessment report was commissioned by the local authorities.

The focus of this project is to describe the different methods used to analyse the behaviour of rockfalls on a slope and its stability taking into account different environmental conditions both present and future. To later apply those to a concrete section of the Vestpynten- Bjørndalen and analyse its stability and the consequence of a rockfall event.

To perform that the section geology was studied to obtain data on the rock characteristics, fractures, strike and dip values and a digital terrain model of the area was produced with a laser scanner. Dangerous rock outcrops were selected and modelled in 2D and their stability analysed employing the SSR method.

Subsequently rockfalls on the same area were simulated to obtain their trajectories, velocity and energy. Two different programs with different approaches to the simulation were employed for this purpose.

The results show a stable slope for present and regular conditions meanwhile different degrees of instability are achieved for future conditions and seismic events.

Regarding rockfalls, under different scenarios the trajectories represent a real threat to the cabins present in the area.

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Table of figures

FIGURE 1GENERAL LOCATION OF THE SVALBARD ARCHIPELAGO IN THE ARCTIC REGION ...1

FIGURE 2THE SVALBARD ARCHIPELAGO (GOOGLE EARTH) ...1

FIGURE 3AVERAGE ANNUAL TEMPERATURE FOR SVALBARD AIRPORT.DOT IS SINGLE YEAR AND BLACK CURVE IS SMOOTHED VARIATION ON A TEN-YEAR SCALE BASED ON OBSERVATIONS FROM 1900 TO 2017.THE RED SECTION SHOWS PREDICTIONS FOR FUTURE CLIMATE SCENARIOS SHOWN WITH RED LINE (MEDIAN) AND DIAMOND (FINE-SCALE MODEL) SHADED AREA SHOWS INTERVAL BETWEEN HIGH AND LOW EMISSIONS SCENARIO FROM (NORSK KLIMASERVICESENTER,METEOROLOGISK INSTITUTT, 2019) ...2

FIGURE 4LOCATION OF WITH THE PROJECT HAS TAKEN PLACE FROM TOPOSVALBARD MODIFIED BY (VIEJO) ...2

FIGURE 5ASPECT OF THE TOP OF THE SLOPE AROUND THE STUDY ZONE (VIEJO) ...3

FIGURE 6ON THE LEFT A BOULDER FOUND ON THE AREA (VIEJO), ON THE RIGHT A LANDSLIDE/DEBRIS FLOW CHANNEL (MULTICONSULT,2017) ...3

FIGURE 7EXTRACT FROM (RUBENSDOTTER,2015) ABOUT THE TYPE OF SURFACE MATERIALS AND THEIR ORIGIN ON THE STUDY AREA OF THE PROJECT ...4

FIGURE 8PHOTO SHOWING THE DEGREE OF CRACKING EXTRACTED FROM (MULTICONSULT,2017) ...4

FIGURE 9RISK MAP FROM (MULTICONSULT,2017) FOR THE AREA OF INTEREST ...5

FIGURE 10MAP SHOWING THE RESULTS OF ROCKFALL AND AVALANCHE EVENTS WITH RUNOUT AREAS FOR THE AVALANCHE IN SHADOWS OF PINK AND STOPPING POINTS FOR ROCKFALLS IN ORANGE WITH RED SIGNALLING MAXIMUM EXTENT (MULTICONSULT,2017) ...5

FIGURE 11PARAMETERS TO DESCRIBE A ROCK MASS FROM (DUNCAN,2018) ...7

FIGURE 12 ANGLE CONDITION FOR PLANE FAILURE (OYANGUREN &MONGE,2004) ... 11

FIGURE 13PLANE FAILURE WITH SCHEMATICS OF THE FORCES INVOLVED (DUNCAN,2018) ... 11

FIGURE 14NORMAL STRESS ON A SLIDING PLANE FROM (DUNCAN,2018) ... 12

FIGURE 15SLIDING PLANE WITH A TRIANGULAR DISTRIBUTION FOR THE PRESSURE IN THE CASE THAT THE WATER TABLE IS BELOW THE BASE OF THE TENSION CRACK (DUNCAN,2018) ... 13

FIGURE 16WEDGE FAILURE FROM (OYANGUREN &MONGE,2004) ... 14

FIGURE 17TYPES OF ANGLE FOR WEDGE FAILURE FROM (DUNCAN,2018) ... 14

FIGURE 18ANGLES AND FORCES PRESENT ON A WEDGE FAILURE FROM (DUNCAN,2018) ... 15

FIGURE 19ABACUS TO OBTAIN THE K FACTOR OF A WEDGE FAILURE (DUNCAN,2018) ... 16

FIGURE 20SCHEME OF A CIRCULAR FAILURE (DUNCAN,2018) ... 17

FIGURE 21LOCATION OF CRITICAL SLIDING SURFACE FOR CIRCULAR SHAPES ON DRAINED SLOPES FROM (DUNCAN,2018) ... 18

FIGURE 22LOCATION OF CRITICAL SLIDING SURFACE FOR CIRCULAR SHAPES ON SLOPES WITH GROUND WATER FROM (DUNCAN,2018) ... 19

FIGURE 23BISHOP'S SLICE METHOD FROM (DUNCAN,2018) ... 20

FIGURE 24JANBU'S SLICE METHOD FROM (DUNCAN,2018) ... 21

FIGURE 25BISHOP'S METHOD FOR NONLINEAR DEFINED MATERIALS (DUNCAN,2018) ... 22

FIGURE 26BLOCK TOPPLING FROM (DUNCAN,2018) ... 23

FIGURE 27FLEXURAL TOPPLING FROM (DUNCAN,2018) ... 23

FIGURE 28BLOCK FLEXURAL TOPPLING FROM (DUNCAN,2018)... 23

FIGURE 29EXAMPLE FOR EXTERNAL FORCES APPLICATION FROM (DUNCAN,2018) ... 25

FIGURE 30LOCATION OF THE CABIN IN THE ANALYSIS AREA.MAP FROM (NORWEGIAN POLAR INSTITUTE) MODIFICATIONS BY (VIEJO) ... 29

FIGURE 31LOCATION OF TERTIARY GEOLOGICAL FORMATIONS (NORWEGIAN POLAR INSTITUTE,2007) ... 29

FIGURE 32STUDY AREA FROM THE CABIN LOCATION (VIEJO) ... 30

FIGURE 33STUDIED ROCK OUTCROPS 1 TO 7 FROM RIGHT TO LEFT ... 30

FIGURE 34A) DISTANCE BETWEEN JOINT FACES B) MOSS AND CLAY WAS PRESENT IN SOME FRACTURES ... 31

FIGURE 35TABLE USED FOR GSI ESTIMATION (DUNCAN,2018) ... 31

FIGURE 36VIEW OF THE LEFT SIDE OF THE FOURTH ROCK OUTCROP ... 32

FIGURE 37SAMPLES COLLECTED FOR THE DENSITY TESTS ... 32

FIGURE 38BUCKET USED AND INSIDE DIAMETER ... 33

FIGURE 39CLOSEUP OF THE ROCK OUTCROPS WITHOUT ANY WATER SIGN ... 34

FIGURE 40WATER FROM MELTING PROCESSES COMING DOWN FROM THE GULLEY ... 35

FIGURE 41LASER SCANNER EMPLOYED TO OBTAIN THE DTM OF THE SLOPE ... 35

FIGURE 42OBTAINED DTM OF THE STUDY AREA ... 36

FIGURE 43STEREONET PROJECTION OF COLLECTED DATA... 37

FIGURE 44DIRECTION OF THE SLOPE DIPPING FOR AREAS 3,4 AND 5... 38

FIGURE 45FLEXURAL TOPPLING STABILITY ANALYSIS FOR A SLOPE OF 76 º WITH A DIRECTION OF 250º ... 38

FIGURE 46FLEXURAL TOPPLING STABILITY ANALYSIS FOR A SLOPE OF 76º WITH A DIRECTION OF 320 º ... 39

FIGURE 47DIRECT TOPPLING ANALYSIS FOR A 76º 250º SLOPE ... 39

FIGURE 48DIRECT TOPPLING ANALYSIS FOR 76º AND 320 º SLOPE ... 40

FIGURE 49STUDY AREAS ON THE DTM REPRESENTATION ... 41

FIGURE 50CAD DRAWINGS OF THE STUDIED SECTIONS A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 42

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FIGURE 51SECTIONS WITH THE JOINT NETWORK APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4

AND 5),E VERTICAL SECTION ... 47

FIGURE 52HIGHLIGHT OF THE MODELLED BLOCK IN SECTION 3... 48

FIGURE 53MODELLED ROCK OUTCROPS WITH APPLIED MESH A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 49

FIGURE 54DISTANCE FROM LONGYEARBYEN (USED AS REFERENCE) TO THE ATLANTIC RIDGE (LANDSAT/COPERNICUS,GOOGLE EARTH) ... 50

FIGURE 55400 NEWEST EARTHQUAKES AROUND THE LONGYEARBYEN AREA (INCORPORATED RESEARCH INSTITURIONS FOR SEISMOLOGY (IRIS),2020) ... 50

FIGURE 56THREE LARGEST EARTHQUAKES SINCE 2010(INCORPORATED RESEARCH INSTITURIONS FOR SEISMOLOGY (IRIS),2020) ... 51

FIGURE 57LOCATION OF THE NORSARSVALBARD STATION ... 51

FIGURE 58SEISMOGRAPHS FOR THE 3 LARGEST EARTHQUAKES SINCE 2010 ... 52

FIGURE 59SECTIONS WITH GROUNDWATER APPLIED IF NECESSARY A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 54

FIGURE 60SECTIONS WITH DRY SOIL IN LIGHT BLUE AND SATURATED SOIL IN GREEN FOR GLOBAL WARMING CONDITIONS, SEPARATED BY THE PIEZOMETRIC LINE IN BLUE A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 55

FIGURE 61MAXIMUM SHEAR STRAIN FOR THE ANALYSED SECTIONS UNDER REAL SEISMIC LOAD A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 57

FIGURE 62TOTAL DISPLACEMENT FOR THE ANALYSED SECTIONS UNDER REAL SEISMIC LOAD A SECTION 3,B SECTION 4,C SECTION 5, D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 58

FIGURE 63MAXIMUM SHEAR STRAIN FOR THE SIMULATED SECTIONS DURING REGULAR SUMMER CONDITIONS WITH IMPROBABLE SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 59

FIGURE 64TOTAL DISPLACEMENT FOR THE SIMULATED SECTIONS DURING REGULAR SUMMER CONDITIONS WITH IMPROBABLE SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 60

FIGURE 65MAXIMUM SHEAR STRAIN FOR THE SIMULATED SECTIONS DURING REGULAR SUMMER CONDITIONS WITHOUT SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 61

FIGURE 66TOTAL DISPLACEMENT FOR THE SIMULATED SECTIONS DURING REGULAR SUMMER CONDITIONS WITHOUT SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 62

FIGURE 67MAXIMUM SHEAR STRAIN FOR THE SIMULATED SECTIONS DURING WARMER CONDITIONS WITH REAL SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 64

FIGURE 68TOTAL DISPLACEMENT FOR THE SIMULATED SECTIONS DURING WARMER CONDITIONS WITH REAL SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 65

FIGURE 69 MAXIMUM SHEAR STRAIN FOR THE SIMULATED SECTIONS DURING REGULAR CONDITIONS WITH IMPROBABLE SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 66

FIGURE 70TOTAL DISPLACEMENT FOR THE SIMULATED SECTIONS DURING WARMER CONDITIONS WITH IMPROBABLE SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 67

FIGURE 71MAXIMUM SHEAR STRAIN FOR THE SIMULATED SECTIONS DURING WARMER CONDITIONS WITHOUT SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 68

FIGURE 72TOTAL DISPLACEMENT FOR THE SIMULATED SECTIONS DURING WARMER CONDITIONS WITHOUT SEISMIC LOAD APPLIED A SECTION 3,B SECTION 4,C SECTION 5,D SECTION 5 CENTRE (BETWEEN 4 AND 5),E VERTICAL SECTION ... 69

FIGURE 73MODEL OF THE SLOPE IN ROCPRO 3D, COLOURS REPRESENT THE DIFFERENT SOILS APPLIED TO THE MODEL ... 74

FIGURE 74ON TOP DETAIL OF THE TERRAIN CLOSE TO THE ROAD IN THE RUN OUT AREA, ON THE BOTTOM GENERAL VIEW OF THE TERRAIN FROM THE SECTION 5 CENTRE ... 75

FIGURE 75RELEASE AREAS ON THE SLOPE ... 76

FIGURE 76DTM GENERATED INSIDE RAMMS ROCKFALL ... 79

FIGURE 77TYPES OF TERRAIN IN RAMMS ROCKFALL (SLF/WSL,2016) ... 80

FIGURE 78POLYGONS USED TO DEFINE THE SOIL TYPES ON THE TERRAIN ... 81

FIGURE 79RELEASE LINES FOR THE RAMMS ROCKFALL SIMULATIONS ... 81

FIGURE 803D MODELS OF THE ROCKS USED FOR THE RAMMSROCKFALL SIMULATIONS ... 82

FIGURE 81ROCPRO SIMULATION RESULTS FOR REGULAR CONDITIONS, TOP KINETIC ENERGY, MIDDLE ROCK VELOCITY, BOTTOM ROCK HEIGHT ... 83

FIGURE 82ROCPRO SIMULATIONS RESULTS AFTER 10 ROUNDS.IN YELLOW THE RELEASE AREAS IN RED THE ROCK TRAJECTORIES .... 84

FIGURE 83ROCK KINETIC ENERGY FOR ACTUAL CONDITIONS, ON TOP SIMULATION WITH ROCK 1 ON THE BOTTOM SIMULATION WITH ROCK 2 ... 85

FIGURE 84ROCK VELOCITY FOR ACTUAL CONDITIONS, ON TOP SIMULATION WITH ROCK 1 ON THE BOTTOM SIMULATION WITH ROCK 2 ... 86

FIGURE 85ROCK HEIGHT FOR ACTUAL CONDITIONS, ON TOP SIMULATION WITH ROCK 1 ON THE BOTTOM SIMULATION WITH ROCK 2 .. 87

FIGURE 86KINETIC ENERGY RESULTS FOR RAMMSROCKFALL ON THE LEFT AND ROCPRO 3D ON THE RIGHT ... 88

FIGURE 87KINETIC ENERGY RESULTS FOR ROCPRO 3D USING SOIL DRAG COEFFICIENTS FROM RAMMSROCKFALL ... 88

FIGURE 88SOIL TYPE LOCATION IN THE ROCPRO 3D MODEL COLOURS REPRESENT THE DIFFERENT SOILS APPLIED ... 89

FIGURE 89POLYGONS USED TO DEFINE THE SOIL TYPES ON THE TERRAIN ... 90

FIGURE 90ROCPRO SIMULATION RESULTS FOR WARMER CONDITIONS, TOP KINETIC ENERGY BOTTOM ROCK VELOCITY ... 91

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FIGURE 91ROCK KINETIC ENERGY FOR WARMER CONDITIONS, ON TOP SIMULATION WITH ROCK 1 ON THE BOTTOM SIMULATION WITH ROCK 2 ... 92 FIGURE 92ROCK VELOCITY FOR WARMER CONDITIONS, ON TOP SIMULATION WITH ROCK 1 ON THE BOTTOM SIMULATION WITH ROCK 2 ... 93 FIGURE 93KINETIC ENERGY RESULTS FOR RAMMSROCKFALL ON THE LEFT AND ROCPRO 3D ON THE RIGHT FOR WARMER

CONDITIONS ... 94

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1

1. Introduction

1.1. The Svalbard archipelago

Svalbard or Spitsbergen is an archipelago located in the arctic region between 74º to 81º N and 10º to 35º E whose sovereignty relies on the kingdom of Norway, see Figure 1

Figure 1 General location of the Svalbard archipelago in the arctic region

Svalbard presents three main settlements as shown in Figure 2, Longyearbyen the biggest one and point of entrance to the island with a population around 2500, Barentsburg a Russian settlement with around 600 inhabitants and Ny-Alesund a research town.

Figure 2 The Svalbard archipelago (Google Earth)

Svalbard

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2 Due to its location, the archipelago’s weather is of arctic nature which is a type of extreme weather characterised by extremely low temperatures, high winds, and periods of complete darkness or daylight (polar night and midnight sun respectively). At the same time on a more global scale its situation means that it is under the influence of the polar amplification effect which accelerates and increases the global warming mechanisms.

Figure 3 shows historical and future predictions for the temperature in Longyearbyen based on different CO2 emission scenarios, extracted from (Norsk Klimaservicesenter, Meteorologisk institutt, 2019)

Figure 3 Average annual temperature for Svalbard airport. Dot is single year and black curve is smoothed variation on a ten-year scale based on observations from 1900 to 2017. The red section shows predictions for future climate scenarios shown with red line (median) and diamond (fine- scale model) shaded area shows interval between high and low emissions scenario from (Norsk Klimaservicesenter, Meteorologisk institutt, 2019)

This project takes place around the Longyearbyen area precisely at a section between Vestpynten and Bjørndalen, along the road that connects Longyearbyen with Bjørndalen, see Figure 4.

Figure 4 Location of with the project has taken place from TopoSvalbard modified by (Viejo)

This area presents steep hillsides, rock outcrops and cliffs seen in Figure 5 which represent a geotechnical hazard.

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3

Figure 5 Aspect of the top of the slope around the study zone (Viejo)

The slope angle on the study zone presents a minimum value of 25 º with a max value of 90 º for the cliff areas and a mean of 65º. For the type of geology in the area, sandstone and shales, slope angles higher than 45º present a probable release area.

At the same time it shows clear sings of mass movements along the years like boulders, debris fans and channels from landslides / debris flow, see Figure 6. This type of deposits had been identified and mapped by the NGU (Norges Geologiske Undersøkelse/Norwegian Geological Survey) in (Rubensdotter, 2015) and the extract corresponding to the study area is shown in

Figure 6 On the left a boulder found on the area (Viejo), on the right a landslide/debris flow channel (Multiconsult, 2017)

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4

Figure 7 Extract from (Rubensdotter, 2015) about the type of surface materials and their origin on the study area of the project

1.2. Previous study

All this section of the coastline is used by the local residents as a leisure place with a lot of cabins present, which, due to the hazards located on the area promoted, the local authorities were interested on its assessment

A study was carried out on behalf of Longyearbyen Lokalstyre by the company Multiconsult (Multiconsult, 2017)

That report covered all of the gravitational processes, but only its findings for rockfalls covering the Vestpynten to Bjørndalen part of the report (the area that is equivalent to the one in this study) are summarized here:

• The entire stretch up to the entrance towards Bjørndalen is characterized by the danger of rockfall. Exposed rock shows a large degree of cracking, see Figure 8 extracted from (Multiconsult, 2017)

Figure 8 Photo showing the degree of cracking extracted from (Multiconsult, 2017)

• In some areas there have been landslides with outlet across the road and down to the shore

• Figure 9 shows the risk map developed by Multiconsult in the (Multiconsult, 2017) report, red shows 1/100 year, orange 1/1000 and yellow 1/5000 type of events areas of influence

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Figure 9 Risk map from (Multiconsult, 2017) for the area of interest

• Figure 10 Shows the results of the simulations conducted by Multiconsult regarding avalanches and rockfalls

Figure 10 Map showing the results of rockfall and avalanche events with runout areas for the avalanche in shadows of pink and stopping points for rockfalls in orange with red signalling maximum extent (Multiconsult, 2017)

From the results of (Multiconsult, 2017) it can be seen that the area presents real risk for the owners of the properties built in place. Despite this the events can be categorized under low probability, as the risk map shows that most of the cabins lay into the 1/1000 years type of event classification.

The report explains future scenarios with warmer conditions and their consequences on the different processes that were assessed on it but is not clear if the obtained risk maps show this condition on the assigned risk value.

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6

1.3. Objective

This master thesis project aims to provide an analysis of the section between Vestpynten and Bjørndalen not only from the rockfall risk point of view but also incorporating an analysis of the stability of that area. While knowing the previous study done in the area and its results.

This will be done by running computer simulations with actual environmental conditions and future warmer environments which could increment the frequency, severity of such events, diminish some and empower others or alter the behaviour of them.

1.4. Rock mass classification systems and strength criteria

When working with rock masses or blocks it is necessary to stablish its mechanical properties which will determine how risk assessment is done and infrastructures built.

This section introduces the main rock mass classification systems and how their parameters are used on the different strength criteria. There are three main classifications used right now, Rock Mass Rating (RMR) from Bieniawski (1973,1976, 1989), Barton’s Q (Barton, Lien, Lunde (1974)) and a modification of the RMR called GSI developed by Hoeck and Brown (1988)

1.4.1. Rock Mass Rating (RMR) Bieniawski (19733, 1976, 1989) The RMR is comprised of six parameters:

1) Compression strength: obtained from tables or from samples tested in a lab

2) RQD: Rock Quality Designation, a measure of the hardness of a rock mass which is inferred from the integrity of a core run when extracted from the borehole. The value is obtained with the following expression:

𝑅𝑄𝐷 =∑ 𝑐𝑜𝑟𝑒 𝑓𝑟𝑎𝑔𝑚𝑒𝑛𝑡𝑠 ≥ 10𝑐𝑚

𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑟𝑒 𝑟𝑢𝑛 ∗ 100

If no core runs are available RQD can be obtained from rock outcrops with the expression:

𝑅𝑄𝐷 = 110 − 2.5𝐽_𝑣 Where Jv is the number of joints per cubic metre

3) Joint spacing: distance between the discontinuity planes, depending to this distance the rock mass has a different designation according to Table 1

Table 1 Deere's classification of joint spacing (1967)

Description Joint spacing Type of rock mass

Really wide >3 m Solid

Wide 1-3 m Massive

Moderately closed 0.3-1 m Blocky

Closed 0.05-0.3 m Fractured

Really closed <0.05 m Crushed

4) Nature of the joints: the joints themselves are described using the following parameters, the values that describe each parameter can be found in

1) Aperture between joint edges

2) Dimensions of the joint following trend and plunge 3) Roughness of the joint edges

4) Strength of the rock at the joint edges 5) Joint filling

5) Presence of water

6) Orientation of the discontinuities

With the first five parameters of the classification and following Table 2 the primary or initial value for the rock mass is obtained. This value is further on adjusted with parameter 6 according to Table 3

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7 Figure 11 is a representation of a rock block with the most important parameters used for geomechanical classifications.

Figure 11 Parameters to describe a rock mass from (Duncan, 2018)

The last adjustment is done with Table 4 using the denomination obtained from parameter 6. The RMR is the result of adding each value together. Table 5 presents the denomination for the rock mass according to its RMR interval.

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8

Table 2 RMR parameters classification translated from (Oyanguren & Monge, 2004)

Parameters Scale

1

Strength of undisturbed

rock

Point load >10 MPa 4-10 MPa 2-4 MPa 1-2 MPa

For these values simple compression

is recommended Simple

compression >250 MPa 100-250 MPa

50-100

MPa 25-50 MPa 5-25

MPa 1-5 MPa

<1 MPa

Value 15 12 7 4 2 1 0

2 RQD 90-100 % 75-90 % 50-75 % 25-50 % <25 %

Value 20 17 13 8 3

3 Joint spacing >2 m 0.6-2 m 0.2-0.6 m 0.06-0.2 m <0.06 m

Value 20 15 10 8 5

4 Joint condition

Very rough, not continuous, closed, rock healthy at

the edges

Slightly rough, <1

mm separation,

slightly weathered rock at the

edges

Slightly rough, <1

mm separation,

very weathered rock at the

edges

Mirror, fault, or joint filling

<5 mm thick or open joints

1-5mm, continuous

joints

Soft filling with thickness >5 mm or

open joints >5 mm continuous joints

Value 30 25 20 10 0

5 Water

Water flow per

10 m of tunnel None <10 l/min 10-25

l/min

25-125

l/min >125 l/min Ratio between

water pressure in the joint/maximum

main stress σ1

0 <0.1 0.1-0.2 0.2-0.5 >0.5

General conditions

Completely dry

Moist

stains Moisty Water

drops Water flow

Value 15 10 7 4 0

Table 3 Relative orientation between cavity axis and joints from (Oyanguren & Monge, 2004) Trend perpendicular to tunnel axis

Trend parallel to tunnel axis

Dip 0-20 º (Independent of trend) Direction towards dip Direction against dip

Dip 45-90 º

Dip 20-45 º

Dip 45-90 º

Dip 20-45 º

Dip 45-90 º

Dip 20-45 º Very

favourable Favourable Regular Unfavourable Very

unfavourable Regular Unfavourable

Table 4 RMR adjustment due to joint orientation from (Oyanguren & Monge, 2004) Direction of

discontinuities trend and plunge

Very favourable Favourable Regular Unfavourable Very unfavourable

Values

Tunnels and

mines 0 -2 -5 -10 -12

Foundations 0 -2 -7 -15 -25

Slopes 0 -5 -25 -50 -60

Table 5 Rock mass classes under RMR criteria translated from (Oyanguren & Monge, 2004)

RMR value 81-100 61-80 41-60 21-40 <20

Number class I II III IV V

Description Very good Good Regular Bad Very bad

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9 1.4.2. Q classification system (Barton et al 1974)

As in a similar way than RMR the Q index relies in 6 parameters:

• RQD

• Jn: number of groups of joints

• Jr: joint roughness

• Ja: joint weathering

• Jw: decreasing factor accounting for water presence

• SRF: stress reduction factor, it depends on the actual tensional state of the rock mass The Q value of the rock mass is obtained by using each parameter on equation 1

𝑄 = 𝑅𝑄𝐷

𝐽_𝑛 ∗ 𝐽_𝑟 𝐽_𝑎 ∗ 𝐽_𝑤

𝑆𝑅𝐹

1

The parameters have a range between the values in Table 6

Table 6 ranges for Q parameters from (Oyanguren & Monge, 2004)

RQD 0-100

Jn 0.5-20

Jr 0.5-4

Ja 0.75-20

Jw 0.05-1

SRF 0.5-20

Due to the length and number of tables that contain the values and characteristics to determine each parameter they are presented in annex 2.

After calculating the Q value, the rock mass can be classified under the types showed on Table 7

Table 7 Type of rock mass under Q index criteria translated from (Oyanguren & Monge, 2004)

Type of rock mass Q value

Exceptionally bad 10^-3-10^-2 Extraordinarily bad 10^-2-10^-1

Very bad 10^-1-1

Bad 1-4

Regular 4-10

Good 10-40

Very good 40-100

Extraordinarily good 100-400 Exceptionally good 400-1000

1.4.3. GSI classification (Oyanguren & Monge, 2004) (Duncan, 2018)

Developed to estimate the mb and s parameters for the Hoek-Brown classification after realising that RMR was not adequate to relate failure criteria to geological observations specially for weak rock masses. The GSI is a modification of the RMR and Q classification as it was considered by Hoek-Brown that some of the parameters used were unnecessary for a breakage criterion. For RMR the discarded parameters are ground water conditions and orientation of the geological structure, in the case of the Q system ground water conditions and stress state SRF. This is due to the fact that on a breaking criterion, calculations are done in effective stresses thus not needing the water pressure. (Oyanguren & Monge, 2004)

GSI index is obtained after a careful visual inspection of the rock mass and it is mainly qualitative, Figure 35 shows the chart used with type of structures, the condition of the discontinuities’ surface and the index assigned as a result applied to the case study of this project.

There are considerations in this index that adjust the assigned value, if the shear strength of the discontinuities is reduced by the presence of water the assigned grade is one less that what it should be. If the

These two parameters are influenced by joint filling and size

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10 analysis is done on a rock surface damaged by blasting activity the index should be moved a column towards the left.

As GSI is based on an isotropic behaviour of the rock mass it cannot be applied to rock masses with a dominant fractured direction, like slate masses, as the difference in strength between the rock and the discontinuities is too small to have an isotropic behaviour. It cannot be used in hard rock masses which present little to no fractures and the ones present have the same longitude as the height of the slope bench in this case the stability depends only on the behaviour of the discontinuity

1.4.4. RMR for rock slopes, SMR index (Oyanguren & Monge, 2004)

The Slope Mass Rating (SMR9 is an adjustment to the RMR developed by Romana in (Romana, 1991) based on the following equation

𝑆𝑅𝑀 = 𝑅𝑀𝑅 − (𝐹₁+ 𝐹₂+ 𝐹₃) + 𝐹₄ ₂

Where

• RMR is the calculated RMR for the rock mass

• 𝐹₁ = [1 − 𝑠𝑖𝑛(𝛼_𝐽− 𝛼_𝑆)]² αj trend angle of discontinuities αs slope trend angle

• 𝐹₂ = (𝑡𝑎𝑛𝛽_𝑗)² βj dip angle of discontinuity if toppling is the most probable failure F2=1

• 𝐹₃ relation between the dip angle of the joint and the rock slope, this value is obtained from Table 8

Table 8 Reduction factor for discontinuity orientation Discontinuity orientation Value

Very favourable 0

Favourable -5

Regular -25

Unfavourable -50

Very unfavourable -60

• 𝐹₄ factor related to the excavation method, slope in natural conditions (natural erosion, vegetation etc) +15, excavated with pre-splitting techniques +10, excavated with smooth blasting techniques +8, excavated with correctly done blasts 0, excavated with faulty blast that could have diminish the stability -8, excavated with rip techniques 0 (as this is only possible on soft rocks the method nor improves neither worsens stability)

This assessment method is indicated for preliminary stages of the project

1.5. Predominant weathering mechanism in arctic climate regions

In temperate climates the weathering mechanisms are a mixture of biological, chemical, and physical processes. In the arctic region the almost all year long sub-zero temperatures make the biological and chemical processes so slow that can be neglected.

Arctic regions are characterized for the presence of permafrost and high availability of water thus the main weathering mechanism are governed by these two factors.

Permafrost is defined as ground that stays below 0º C for two consecutive years

1.6. Slope failure modes and analyses

There are two developed methods or models to describe and analyse the stability and mode of failure of a slope: the limit equilibrium analysis (LEA) and the shear strength reduction (SSR). For the purpose of this project only the SSR method has been used for the subsequent analysis.

Limit equilibrium analysis had been the standard in the industry since its conception and are still used nowadays due to its reliability and number of cases analysed around the world which provides cases to study.

The shear strength reduction method has started to gain popularity due to its powerfulness and flexibility while at the same time computers had become more powerful making this method time-cost effective.

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11 In this section first LEA is going to be described for each of the different types of slope failure, secondly the SSR will be explained in general as it doesn’t have different approaches depending on the type of failure mechanism as the LEA has.

1.6.1. Limit equilibrium analysis (LEA) methods

Plane (Duncan, 2018) (Oyanguren & Monge, 2004)

The plane failure is an uncommon type of failure as the required geometrical conditions are rarely met.

Being the simplest mechanism, it is easy to understand failure concepts that will be more complicated on the complex failure types.

The conditions for this failure to happen are

• The strike of the sliding plane must be parallel with a ±20 º difference to the slope face

• The dip of the sliding plane must be less than the dip of the slope face 𝛹_𝑝 < 𝛹_𝑓 check Figure 12

• The dip of the plane must be larger than the angle of friction 𝛹_𝑝 > 𝜙 check Figure 12

Figure 12 angle condition for plane failure (Oyanguren & Monge, 2004)

• The upper end of the sliding surface either intersects the upper slope, or terminates in a tension crack

• The presence of another two discontinuities that create lateral release surfaces that represent the lateral boundaries.

To analyse this failure the case used is the one with a tension crack in the upper surface of the slope as seen in Figure 13

Figure 13 Plane failure with schematics of the forces involved (Duncan, 2018)

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12 As assumptions:

• The sliding surface and tension crack strike parallel to the slope

• The tension crack is filled with water up to zw

• The water pressure is represented by the greyed-out area in the force schematics on Figure 13

• The forces are supposed to act in the centroid of the mass thus producing no moments, the error introduced by this is neglectable if not used in steep slopes with steeply dipping discontinuities.

• The shear strength of the sliding surface is defined by 𝜏 = 𝑐 + 𝜎𝑡𝑎𝑛𝜙 as the Mohr-Coulomb criteria. On a rough surface the apparent cohesion and friction angle are a tangent that takes into account the normal stress σ on the sliding surface, this stress can be obtained from the curves in Figure 14.

Figure 14 Normal stress on a sliding plane from (Duncan, 2018)

• There is no resistance on the lateral boundaries of the sliding block

• As the analysis is by-dimensional the area is represented by the length of the surface and the volume as the cross-section area of the block, due to the consideration of a slice of unit thickness at right angles to the slope face.

The factor of safety is FS is obtained as the ration between the resisting force and the driving force on equation 3

𝐹𝑆 =𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑛𝑔𝑓𝑜𝑟𝑐𝑒

𝐷𝑟𝑖𝑣𝑖𝑛𝑔𝑓𝑜𝑟𝑐𝑒 =𝑐 ∗ 𝐴 + ∑ 𝑁 ∗ 𝑡𝑎𝑛𝜙

∑ 𝑆 ³

Where c is cohesion, A is area of the sliding block, ∑ 𝑁 sum of the normal forces, ϕ angle of friction and

∑ 𝑆 sum of the shearing forces.

Using the example from Figure 13 equation 3 can be written as

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13 𝐹𝑆 =𝑐 ∗ 𝐴 + (𝑊 ∗ cos 𝜓_𝑝− 𝑈 − 𝑉 ∗ sin 𝜓_𝑝) ∗ tan 𝜙

𝑊 ∗ sin 𝜓_𝑝+ 𝑉 ∗ cos 𝜓_𝑝 ⁴

A can be obtained from equation 5

𝐴 = (𝐻 + 𝑏 ∗ 𝑡𝑎𝑛(𝛹_𝑠) − 𝑧) ∗ 𝑐𝑠𝑐(𝛹_𝑝) ₅ Where H is height of the slope, b is the distance behind the slope crest at which the crack is located, z is crack depth, Ψs is the dip of the slope above the crest

As the crack is full of water up to a depth of zw, U is the force in the sliding plane and V is the force in the tension crack. These forces can be calculated with equations 6 and 7

𝑈 = 1

2𝛾_𝑤 ∗ 𝑧_𝑤∗ (𝐻 + 𝑏 ∗ 𝑡𝑎𝑛(𝛹_𝑠) − 𝑧) ∗ 𝑐𝑠𝑐 (𝛹_𝑝) 6

𝑉 = 1

2𝛾_𝑤 ∗ 𝑧_𝑤² 7

𝛾_𝑤 is the unit weight of water

The weight of the block W is obtained with equation 8 𝑊 =1

2𝛾_𝑟∗ 𝐻²[(1 − 𝑧 𝐻)

2

∗ cot 𝜓_𝑝(cot 𝜓_𝑝∗ tan 𝜓_𝑓− 1] ₈ 𝛾_𝑟 is the unit weight of the rock, 𝜓_𝑓is the slope face angle, 𝜓_𝑝 is dip angle of the sliding plane

Particularising this case for the arctic region focusing on the ground water effects, during the melting season water runs into the cracks of the rock, building water pressure but this can be close to zero if the remaining rock mass is impermeable or the sliding plane contains a clay filling that has low conductivity. For this case U=0 and V is calculated with equation 7. In the case that the ground water cannot be discharged due to freezing conditions on the rock mass the uplift pressure can be approximated by a rectangular distribution with equation 9

𝑈 = 𝐴 ∗ 𝑝 ₉

Where A is the area of the sliding plane, equation 5, and p is the hydrostatic pressure obtained with equation 10

𝑝 = 𝛾_𝑤∗ 𝑧_𝑤 ₁₀

This case is shown in Figure 15

Figure 15 Sliding plane with a triangular distribution for the pressure in the case that the water table is below the base of the tension crack (Duncan, 2018)

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14 One of the first symptoms to detect a block that is getting close to instability is the appearance of the explained tension cracks on the slope crest. This appears as a result of small movements on the rock mass with an accumulative effect, when the tension crack surfaces it can be supposed that shear failure has initiated.

Wedge (Duncan, 2018) (Oyanguren & Monge, 2004)

Type of failure controlled by two or more discontinuities characteristic of strong rock masses with well- defined discontinuities.

A wedge failure occurs when two planar discontinuities that strike obliquely to the face met on an intersection line creating a block that will slide along such intersection. Figure 16 shows a representation of this type of failure.

Figure 16 Wedge failure from (Oyanguren & Monge, 2004)

The conditions for a wedge failure are:

• Existence of two planes that intersect in a line, defined by its trend 𝛼_𝑖 and plunge 𝛹_𝑖

• The plunge of the intersection must be flatter than the dip of the face but higher than the angle of friction of both planes that define it 𝛹_𝑓 > 𝛹_𝑖 > 𝜙 as shown in Figure 17

Figure 17 Types of angle for wedge failure from (Duncan, 2018)

• The line of intersection must dip outwards the face for the sliding to occur. The range is between 𝛼_𝑖 and 𝛼_𝑖^′

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15 To obtain the trend 𝛼_𝑖 and plunge 𝛹_𝑖 of the intersection between planes A and B equation 11 and 12 are used.

𝛼_𝑖 = 𝑡𝑎𝑛⁻¹(𝑡𝑎𝑛(𝛹_𝐴) ∗ 𝑐𝑜𝑠(𝛼_𝐴) − 𝑡𝑎𝑛(𝛹_𝐵) ∗ 𝑐𝑜𝑠 (𝛼_𝐵)

𝑡𝑎𝑛(𝛹_𝐵) ∗ 𝑠𝑖𝑛(𝛼_𝐵) − 𝑡𝑎𝑛(𝛹_𝐴) ∗ 𝑠𝑖𝑛 (𝛼_𝐴)) ₁₁ 𝛹_𝑖 = 𝑡𝑎𝑛⁻¹(tan(Ψ_𝐴) ∗ cos(𝛼_𝐴− 𝛼_𝑖)) = 𝑡𝑎𝑛⁻¹(tan(Ψ_𝐵) ∗ cos(𝛼_𝐵− 𝛼_𝑖)) ₁₂ 𝛼 and 𝛹 are the trend and dip of the planes A and B that form the wedge, equation 11 gives two solutions separated by 180º, the correct value sits between 𝛼_𝐴 and 𝛼_𝐵

The factor of safety on a wedge failure assuming the same friction angle 𝜙 for both planes is defined by equation 13

𝐹𝑆 = (𝑅_𝐴+ 𝑅_𝐵) ∗ 𝑡𝑎𝑛(𝜙)

𝑊 ∗ 𝑠𝑖𝑛 (𝛹_𝑖) ¹³

RA and RB are the normal reactions from the planes 𝑊 ∗ 𝑠𝑖𝑛 (𝛹_𝑖) is the component of the weight along the intersection line.

The reactions are decomposed into normal and parallel with equations 14 and 15.

𝑅_𝐴∗ 𝑠𝑖𝑛 (𝛽 −1

2∗ 𝜉) = 𝑅_𝐵∗ 𝑠𝑖𝑛 (𝛽 +1

2∗ 𝜉) ₁₄

𝑅_𝐴∗ 𝑐𝑜𝑠 (𝛽 −1

2∗ 𝜉) + 𝑅_𝐵∗ 𝑐𝑜𝑠 (𝛽 +1

2∗ 𝜉) = 𝑊 ∗ 𝑐𝑜𝑠𝛹_𝑖 15

The definition of the angles used in equations 14 and 15 can be found in Figure 18

Figure 18 Angles and forces present on a wedge failure from (Duncan, 2018)

RA and RB are obtained with equation 16

𝑅_𝐴 + 𝑅_𝐵 = 𝑊 ∗ 𝑐𝑜𝑠(𝛹_𝑖) ∗ 𝑠𝑖𝑛(𝛽) 𝑠𝑖𝑛 (𝜉

2)

16

Introducing equation 16 into equation 13 gives equation 17

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16 𝐹𝑆 =

𝑠𝑖𝑛(𝛽) 𝑠𝑖𝑛 (𝜉

2)

∗ 𝑡𝑎𝑛(𝜙) 𝑡𝑎𝑛(𝛹_𝑖)

17

The wedge failure can be related to the plane failure through equation 18

𝐹𝑆_𝑊 = 𝐾 ∗ 𝐹𝑆_𝑃 ₁₈

Where FSw is the factor of safety for the wedge failure supported by friction and FSp is the factor of safety for a plane failure that has the same 𝛹_𝑖 as the intersection, K is a wedge factor that depends on 𝜉 and β which can be obtained from the abacus in Figure 19

Figure 19 Abacus to obtain the K factor of a wedge failure (Duncan, 2018)

Circular (Duncan, 2018)

When the terrain is comprised of soil, debris or low quality and highly weathered rock mass the failure occurs through the whole mass following the line of least resistance. This type of failure is common in mine tailing dams, road slopes and natural slopes.

The failure occurs along a surface of failure with an approximately circular and concave shape that passes through the toe of the slope as shown in Figure 20

Review of rock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjørndalen (Svalbard)

Master ’s thesis

David Viejo Mariño

Review of rock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjorndalen

(Svalbard)

David Viejo Mariño

Review of rock stability models, slope stability and rockfall assessment for a section of Vestpynten-Bjorndalen

(Svalbard)

Acknowledgments

Abstract

Table of contents

Table of figures

1. Introduction

1.1. The Svalbard archipelago

1.2. Previous study

1.3. Objective

1.4. Rock mass classification systems and strength criteria

1.5. Predominant weathering mechanism in arctic climate regions

1.6. Slope failure modes and analyses